[Other] formula for the relationship between attenuation and distance of Wi-Fi wireless signal transmission [Indoor positioning]

Formula for the relationship between attenuation and distance of Wi-Fi wireless signal transmission [Indoor Location]

Calculation of wireless communication distance

1. DBM dbmv dbuv Conversion Relationship
DBM = 10log (pout/1 MW), where pout is the power value in the unit of MW
Dbmv = 20log (Vout/1mV), where Vout is the voltage value in the unit of MV
Dbuv = 20log (Vout/1uv), where Vout is the voltage value in the unit of UV
Conversion Relationship:
Pout = Vout × Vout/R
Dbmv = 10log (R/0.001) + dBm, r is the load impedance
Dbuv = 60 + dbmv

2. Calculation of wireless communication distance
The calculation method of the wireless communication distance during free-space propagation is provided here. The so-called free-space propagation refers to the Radio Wave Propagation when the antenna is surrounded by an infinite vacuum. It is an ideal propagation condition. When a radio wave is transmitted in free space, its energy is neither absorbed by obstacles nor reflected or scattered.
The communication distance is related to the transmit power, receive sensitivity, and operating frequency.
[LFS] (db) = 32.44 + 20lgd (Km) + 20lgf (MHz)
In the formula, LFS is the transmission loss, D is the transmission distance, and the frequency unit is calculated in MHz.

It can be seen from the above that the electrical wave propagation loss (also called attenuation) in free space is only related to the working frequency F and the propagation distance D. When f or D is doubled, [LFS] will add 6db respectively.
The following formula describes the loss of Radio Wave Propagation in free space.
Los = 32.44 + 20lg D (km) + 20lg F (MHz)
Los is the propagation loss, measured in dB.
D is the distance, in the unit of KM
F is the operating frequency, in MHz

The following example shows the propagation distance of a system with a working frequency of 433.92 MHz, a transmit power of + 10dBm (10 MW), and a receiving sensitivity of-105dbm in free space:
1. The receiving sensitivity is-105dbm with the transmit power + 10dBm.
Los = 115db
2. From Los, F
Calculated d = 30 km

This is the ideal transmission distance, which is lower than this value in actual application. This is because wireless communication is affected by various external factors, for example, the loss caused by atmospheric, barrier, and multi-path, the above loss reference value can be included in the formula to calculate the approximate communication distance.
Assuming that the loss caused by atmospheric and occlusion is 25 dB, the communication distance is calculated as follows:
D = 1.7
Conclusion: for every 6 dB increase in wireless transmission loss, the transmission distance is doubled.

Iii. Concept of RF/Transmission Line

Some concepts of transmission lines 3.1

The cable connecting the output end of the antenna and the transmitter (or receiver input end) is called a transmission line or a feeder. The main task of transmission lines is to effectively transmit signal energy. Therefore, it should be able to transmit the signal power sent by the transmitter to the input end of the transmitting antenna at minimum loss, or transmit the signal received by the antenna to the receiver's input end with minimal loss, and it should not pick up or generate stray interference signals. In this way, the transmission line must be shielded. By the way, when the physical length of the transmission line is equal to or greater than the wavelength of the transmitted signal, the transmission line is also called a long line.
3.2 Transmission Line types:
There are two types of transmission lines in the ultra-short wave segment: Parallel dual-line transmission lines and coaxial cable transmission lines;
Microwave band transmission lines include coaxial cable transmission lines, waveguide and micro-strip.
A parallel dual-line transmission line consists of two parallel wires. It is a symmetric or balanced transmission line, which has a high loss and cannot be used in the ultra-high frequency band.
The two wires of the coaxial cable transmission line are core wires and shielded copper wires. Because of copper wires, the two conductors are asymmetrical to the ground. Therefore, they are called asymmetric or unbalanced transmission lines. The coaxial cable has a wide operating frequency and a low loss, which can shield static coupling, but it cannot interfere with the magnetic field. Do not go in parallel with a line with strong current or close to a low-frequency signal line.
3.3 Transmission Line Characteristic Impedance: the ratio of voltage to current in each area of the infinite long transmission line is defined as the characteristic impedance of the transmission line, expressed in z0.
The formula for calculating the characteristic impedance of the coaxial cable is as follows:
Z. = [60/√ ε r] × log (D/d) [Euro].
Type, D is the outer diameter of the copper wire of the coaxial cable;
D is the outer diameter of the coaxial cable core;
ε r is the relative dielectric constant of the insulating medium between conductors.
Generally, z0 = 50 euro, and z0 = 75 Euro. It is not difficult to see from the above formula that the characteristic impedance of the feeder is only related to the diameter D and D of the conductor and the dielectric constant ε r of the medium between the conductors, it has nothing to do with the length of the feeder, the operating frequency, and the load impedance of the feeder terminal.
3.4 feeder attenuation coefficient: signal transmission in the feeder, in addition to the resistance loss of the conductor, there is also the dielectric loss of insulation materials. The loss increases with the length of the feeder and the working frequency. Therefore, reasonable layout should be made to shorten the length of the feeder as much as possible. The loss produced per unit length is represented by the attenuation coefficient: β, and the Unit is dB/M (decibel/meter ), most units in the cable Technical Specification use dB/100 m (dB/M ).
If the input power to the feeder is P1 and the output power from the feeder with a length of L (m) is P2, the transport loss TL can be expressed:
TL = 10 × lg (P1/P2) (db)
Attenuation coefficient is Beta = TL/L (dB/m)
For example, for Nokia 7/8 inch low-consumption cable, the attenuation coefficient of 900 MHz is β = 4.1 dB/100 m, and can also be written as β = 3 dB/73 m, that is, the signal power at a frequency of MHz is half the power of a 73 m long cable. Ordinary non-low-consumption cables, for example,
SYV-9-50-1, 900 MHz attenuation coefficient is Beta = 20.1 dB/100 m, can also be written as beta = 3 dB/15 m, that is, the frequency is 900 MHz signal power, each time the cable goes through 15 m, the power will be less than half!
3.5 Transmission Line impedance matching and reflection loss: when the load impedance ZL received by the feeder terminal is equal to the feeder Characteristic Impedance z0, it is called that the end of the feeder is connected by matching. When matching, There is only an incident wave of the incoming terminal load on the feeder, but no reflection wave generated by the terminal load. Therefore, when the antenna acts as the terminal load, matching ensures that the antenna obtains all signal power. When the Antenna Impedance is 50 euro, it is matched with the 50 euro cable, and when the Antenna Impedance is 80 euro, it is not matched with the 50 euro cable. If the antenna vibrator diameter is coarse and the input impedance of the antenna changes little with the frequency, it is easy to maintain matching with the feeder. At this time, the operating frequency of the antenna is wider. Otherwise, it is narrow.
In practice, the input impedance of the antenna is also affected by the surrounding objects. In order to make the feeder and antenna match well, it is necessary to adjust the local structure of the antenna through measurement when setting up the antenna, or install a matching device.
It has been pointed out that when the feeder and the antenna match, there is no reflection wave on the feeder, and only the incident wave is transmitted, that is, only the wave traveling to the antenna. At this time, the voltage amplitude and current amplitude of each part on the feeder are equal, and the impedance of any point on the feeder is equal to its characteristic impedance. When the antenna and the feeder do not match, that is, the antenna impedance is not equal to the feeder characteristic impedance, the load can only absorb some of the high-frequency energy transmitted on the feeder, but not all of the energy, the unabsorbed part of the energy will be reflected back to form a reflection.
Iv. Boundary loss of the Standing Wave Ratio Reflection Coefficient
4.1 Standing Wave Ratio: it is the reciprocal of the traveling wave coefficient. Its value ranges from 1 to infinity. The standing wave ratio is 1, indicating full match; the standing wave ratio is infinite, indicating total reflection and full mismatch. In mobile communication systems, it is generally required that the standing wave ratio be less than 1.5, but in practical applications, the VSWR should be less than 1.2.
4.2 ripple loss: it is the reciprocal of the absolute value of the reflection coefficient, expressed in decibels. The return loss value ranges from 0 dB to infinity. The larger the return loss, the worse the match. The larger the return loss, the better the match. 0 indicates total reflection, and infinity indicates that it is completely matched in the same phase of the incident wave and the reflected wave. The voltage amplitude is added to the maximum voltage amplitude Vmax to form a wave belly; in contrast to the reflected wave, the voltage amplitude is reduced to the minimum voltage amplitude Vmin, forming a waveform. The amplitude values of other points are between the center of the left-side and the knots. This synthetic wave is called a standing wave.
4.3 The ratio of the reflected voltage to the voltage amplitude of the incident wave is called the reflection coefficient, which is recorded as R.
Reflected amplitude (ZL-Z0)
R = ── ─
Incident wave amplitude (zl + z0)
The ratio of the bandwidth to the voltage amplitude is called the standing wave coefficient, also called the voltage standing wave ratio.
V max (1 + r)
VSWR = ── ─ = ──
Waveform voltage degree Vmin (1-R)

Note: WiFi is used in microwave frequencies. Therefore, when designing a Wi-Fi wireless network, you can refer to the microwave engineering design. For details, refer:
1, "microwave engineering": http://bbs.itgoal.com/viewthread.php? Tid = 63498 & Highlight = % Ce % A2 % B2 % A8 % B9 % A4 % B3 % CC
2. Wireless Communication from Standford: http://bbs.itgoal.com/viewthread.php? Tid = 311 & Highlight = wireless % 2 bcommunication
3. Antenna basic knowledge and application: http://bbs.itgoal.com/viewthread.php? Tid = 8311 & Highlight = % CC % EC % CF % DF